## Section: New Results

### Translating between implicit and explicit versions of proof

Participants : Roberto Blanco, Zakaria Chihani, Dale Miller.

As we have demonstrated within the Parsifal team, the Foundational
Proof Certificate (FPC) framework can be used to define the semantics
of a wide range of proof evidence.
We have given such definitions for a number of textbook proof
systems as well as for the proof evidence output from some existing
theorem proving systems.
An important decision in designing a proof certificate format is the
choice of how many details are to be placed within certificates.
Formats with fewer details are smaller and easier for theorem provers
to output but they require more sophistication from checkers since
checking will involve some proof reconstruction.
Conversely, certificate formats containing many details are larger
but are checkable by less sophisticated checkers.
Since the FPC framework is based on well-established proof theory
principles, proof certificates can be manipulated in meaningful ways.
In fact, we have shown how it is possible to automate moving
from implicit to explicit (*elaboration*) and from explicit
to implicit (*distillation*) proof evidence via the proof
checking of a *pair of proof certificates*.
Performing elaboration makes it possible to transform a proof
certificate with details missing into a certificate packed with enough
details so that a simple kernel (without support for proof
reconstruction) can check the elaborated certificate.
This design allows us to trust in only a single, simple checker of
explicitly described proofs but trust in a range of theorem provers
employing a range of proof structures.
Experimental results of using this design appear in